In the prior art, it is known to perform build-up and draw-down tests to evaluate the condition of the near wellbore area of a reservoir and the inflow rates of the well. These tests can consume from days to weeks to perform. The pressure is either built up (i.e. Homer plot) or permitted to fall off. The pressure response is analyzed at the tail end of the test, as it approaches steady state.
In the drill-stem test, still used regularly in the industry today, gas is vented from the wellhead through an orifice and the flow rate is measured. The measured flow rate out of the wellhead is presumed to be directly attributable to the flow into the well from the reservoir. Unfortunately, one cannot know the inflow rate based on the outflow alone. If a larger orifice is chosen, the observed rate will be misleadingly higher. If the orifice is smaller, the observed rate can be misleadingly and pessimistically lower. These results are dependent not upon the reservoir performance but instead on the throughput of the orifice at the observed surface pressure. In the most obvious case of misinformation, if the observed pressure is changing while venting then the measured outflow cannot equal the inflow. Even more difficult to assess is for the case of gas-free liquid entering the well where substantially only liquid-displaced gas will be measured as outflow.
In related prior art, known as closed-chamber testing, particular characteristics of a well can be determined without prolonged discharge from the well, as disclosed in U.S. Pat. No. 4,123,937 issued to the applicant. This reference discloses a method of determining annular gas rates and gas volume in the well annulus by measuring the change in pressure during blocked flow and briefly flowing a measured amount of gas from the well. Depending upon and assuming a linear rate of change of pressure, gas flow is calculated as a function of the ratio of the gas flow to the rate of pressure change using mass balance techniques. This prior art method of alternately blocking and permitting annular flow is applied to pumping wells as a means for determining the annulus gas rate without causing a significant change in the bottom hole pressure (usually less than about 10 kPa). With little change in the bottom-hole pressure, the reservoir response is not affected.
In U.S. Pat. No. 4,123,937, the pressure during the flow of gas from the well's annulus is observed. This rate of pressure decline during gas flow is assumed to be linear. Due to the short test duration and lack of reservoir involvement, the approximation is usually sufficient.
As described in the prior art, for any gas-filled space, a general equation for the behavior of gases, which will be familiar to those skilled in the art, can be derived, which has many applications within the oil and gas industry, one of which is the subject of the method according to the present invention.
Generally, nomenclature used is as follows:
M=molecular weight of gas PA1 W=mass of the gas (kg) PA1 P=pressure (kPa abs.) PA1 Q.sub.1 or Q.sub.in =gas flowrate into a system (m.sup.3 /d) PA1 Q.sub.2 or Q.sub.out =gas flowrate out of a system (m.sup.3 /d) PA1 T=temperature (deg. K) PA1 V=original gas volume of system, before testing (m.sup.3) PA1 n=the number of moles PA1 R=the universal gas constant PA1 z=gas deviation factor PA1 dP/dt=rate of change of pressure (kPa/min) PA1 dV/dt=rate of change of volume (m.sup.3 /min) PA1 F=Prover (orifice) plate coefficient. PA1 G=Gas gravity PA1 Subscript sc=standard conditions PA1 (a) blocking the wellhead and measuring wellhead pressure over time; PA1 (b) briefly flowing gas from the wellhead and measuring wellhead pressure over time, the duration of gas flow being insufficient to affect the reservoir; PA1 (c) determining the original wellbore gas volume and an original fluid inflow rate as a function of the change of pressure and the original gas volume assuming all of the fluid inflow from the reservoir is gas and the original gas volume remains constant, preferably using an exponential relationship to determine the change in pressure while the wellhead is flowing; then PA1 (d) flowing gas from the wellhead for a prolonged duration, while measuring the wellhead gas flow and measuring the wellhead pressure over time, the duration of gas flow being sufficient to affect the reservoir; PA1 (e) determining the total rate of fluid inflow from the reservoir as a function of the change in pressure in the wellbore, the rate of flow from the wellhead, and the original gas volume assuming the original gas volume remains constant throughout step (d); and finally PA1 (f) determining the incremental inflow rate of fluid from the reservoir as being the difference between the total rate of fluid inflow less the original rate of gas flow.
Simply, PV=nRTz and by replacing the number of moles n, with the weight of the gas divided by the molecular weight of the gas, the equation can then be rewritten as ##EQU1##
where W is the mass of the gas in the system in kilograms.
Similarly, the density of the gas in kg/m.sup.3 can be written as ##EQU2##
The mass rate in or out is equivalent to the flow rate of gas in standard m.sup.3 /min multiplied by the density in kg/m.sup.3. Mathematically, this mass rate is expressed as ##EQU3##
and similarly ##EQU4##
where Q.sub.1 and Q.sub.2 are defined as the gas flowrate in and out of the wellbore respectively.
In order to have a mass balance the rate of change of mass in the system must be equal to the difference between the mass rate in and the mass rate out. Mathematically, this rate of change is expressed as the change in mass in the system over time=mass rate in-mass rate out, or ##EQU5##
If we assume that T and z are constant, then this equation can then be differentiated as follows ##EQU6##
The units on both sides of the equation are in m.sup.3 /min. If we express Q.sub.1 and Q.sub.2 in m.sup.3 /day then the left side of the equation must be divided by 1440 minutes per day. If T.sub.sc =275.15+15 degrees Kelvin and P.sub.sc =101.325 kPa, then the equation can be expressed as: ##EQU7##
The above equation (1) therefore can be considered to be the fundamental equation that satisfies the mass balance of a system and can be used as a steppingstone in evaluating oil and gas wells, flowing or pumping. The derivation of this fundamental equation has been previously disclosed in U.S. Pat. No. 4,123,937 and can be used as the starting point in the development of additional processes to support the new method of testing.